Calculating the volume of individual solution(s) [Mole/Atoms Concept]

[jisbon]

Homework Statement

80 g solid $SiO_{2}$ is made by mixing liquid tetraethyl orthosilicate
$(Si(OC_{2}H_{5})_{4})$, ethanol $(C_{2}H_{5}OH)$, and water at room temperature to form a
solution. The total volume of the solution is 700 ml. The ratio of the number of
water molecules to that of Si atoms is 4:1. The solution is then processed, which
involves various heat treatments, to form solid $SiO_{2}$. The mass densities of $SiO_{2}$,
$(Si(OC_{2}H_{5})_{4})$, $(C_{2}H_{5}OH)$ and water are 2.2 g/cm3, 0.934 g/cm3, 0.801 g/cm3 and 1g/cm3, respectively. Assume that all Si atoms have been converted to $SiO_{2}$.
Calculate the volume of tetraethyl orthosilicate, ethanol and water in the solution (give
your answer in ml).

Relevant Equations

amt = mass/mr
density = mass/volume
no. of atoms = amt * $(6.02*10^{23})$

My answer seems to be way-off/improbable, so I figured something is wrong with it.

From the periodic table,
Mr of tetraethyl orthosilicate = 208.33
Mr of ethanol = 46.069
Mr of water = 18.015
Mr of SiO2 = 60.084

Let the volume of tetraethyl orthosilicate, ethanol and water be x,y,z ml respectively.
x + y + z =700 --- (1)
Since density = mass/volume,

Mass of tetraethyl orthosilicate = 0.934x
Mass of ethanol = 0.801y
Mass of water = z

Since the mass of SiO2 is 80g, can I assume the mass of the above solutions equates to 80g?

If I can:

0.934x+0.801y+z = 80? --- (2)

Also, since ratio of water molecules to Si atoms is 4:1,
No. of Si atoms = amt of Si * (6.02*10^23)
= 0.934x/208.33 * (6.02*10^23)
= 2.69*10^21 x
Amt of water = z/18.015

z= 0.3219x ---- (3)

Solving equations 1,2 and 3,

my values are weird and definitely incorrect (there were some negatives).

Any ideas? Cheers

 

[Borek]

Since the mass of SiO2 is 80g, can I assume the mass of the above solutions equates to 80g?

No, it is much higher, as it contains much more than just SiO₂.

Think about the stoichiometry of the process.

 

[jisbon]

No, it is much higher, as it contains much more than just SiO₂.

Think about the stoichiometry of the process.

Am I supposed to construct an equation for this? I wasn't taught any forms of them and hence not sure about this :/

 

[mjc123]

You are told all you need. You have 80 g SiO₂ - how many moles is that? How many moles of Si atoms? So how many moles of TEOS? What is the mass of TEOS? The volume? How many moles of water? Mass? Volume? Volume of ethanol?
(Note: this assumes no volume change on mixing, which isn't true, but you have to assume it to answer the question.)

 

[jisbon]

You are told all you need. You have 80 g SiO₂ - how many moles is that? How many moles of Si atoms? So how many moles of TEOS? What is the mass of TEOS? The volume? How many moles of water? Mass? Volume? Volume of ethanol?
(Note: this assumes no volume change on mixing, which isn't true, but you have to assume it to answer the question.)

Amount of SiO₂ is 80/60.084 = 1.331 mol
This means there are 1.331 mol of Si atoms, which in turn mean 1.331 mol of TEOS?

 

[mjc123]

OK so far

 

[jisbon]

OK so far

Alright. So with 1.331 mol of TEOS, I can find the volume of it by:
Mass of TEOS = Mr * amt
= 208.33*1.331
Volume of TEOS = 208.33*1.331/2.2 = 126.03ml

Amt of water = 4*1.331
Mass = 18.015*4*1.331
Volume of water = (18.015*4*1.331)/1=95.91ml
Volume of ethanol = 700 - 126.03-95.91?

thanks

 

[mjc123]

Right. All you're missing is the final answer.

 

[Borek]

Note: equivalence between moles of SiO₂ and TEOS means you just followed stoichiometry - you don't need exact reaction equation for that, you need just a ratio of the substances involved.

 

[chemisttree]

Am I supposed to construct an equation for this? I wasn't taught any forms of them and hence not sure about this :/

At your school you are being taught stoichiometry before learning chemical equations? I’ve taught HS chemistry, AP and pre-AP chemistry and that NEVER happened! You have my sympathies!

 

[jisbon]

At your school you are being taught stoichiometry before learning chemical equations? I’ve taught HS chemistry, AP and pre-AP chemistry and that NEVER happened! You have my sympathies!

Thing is this course I am currently learning is actually under Engineering: Intro to materials. So I didn't really have any chemistry background hahas :(